Efficient semiclassical approach for time delays
arXiv:1409.1532 · doi:10.1088/1367-2630/16/12/123018
Abstract
The Wigner time delay, defined by the energy derivative of the total scattering phase shift, is an important spectral measure of an open quantum system characterising the duration of the scattering event. It is related to the trace of the Wigner-Smith matrix Q that also encodes other time-delay characteristics. For chaotic cavities, these exhibit universal fluctuations that are commonly described within random matrix theory. Here, we develop a new semiclassical approach to the time-delay matrix which is formulated in terms of the classical trajectories that connect the exterior and interior regions of the system. This approach is superior to previous treatments because it avoids the energy derivative. We demonstrate the method's efficiency by going beyond previous work in studying the time-delay statistics for chaotic cavities with perfectly connected leads. In particular, the universality for moment generating functions of the proper time-delays (eigenvalues of Q) is established up to third order in the inverse number of scattering channels for systems with and without time-reversal symmetry. Semiclassical results are then obtained for a further two orders. We also show the equivalence of random matrix and semiclassical results for the second moments and for the variance of the Wigner time delay at any channel number.
50 pages, 8 figures
References in corpus (19)
- Semiclassical Foundation of Universality in Quantum Chaos
- Periodic-Orbit Theory of Universality in Quantum Chaos
- Periodic-Orbit Theory of Level Correlations
- Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
- Semiclassical Theory of Chaotic Conductors
- Periodic-orbit theory of universal level correlations in quantum chaos
- Semiclassical Approach to Chaotic Quantum Transport
- Systematic approach to statistics of conductance and shot-noise in chaotic cavities
- Nonlinear statistics of quantum transport in chaotic cavities
- Ehrenfest time dependent suppression of weak localization
- Delay times and reflection in chaotic cavities with absorption
- Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
- Integrable theory of quantum transport in chaotic cavities
- Full counting statistics of chaotic cavities from classical action correlations
- Full counting statistics of chaotic cavities with many open channels
- Is the concept of the non-Hermitian effective Hamiltonian relevant in the case of potential scattering?
- Statistics of thermal to shot noise crossover in chaotic cavities
- Semiclassical Mechanism for the Quantum Decay in Open Chaotic Systems
- Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard